Economics and Computer Science

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Economics and Computer Science

• CS595, SB 213
• Xiang-Yang Li
• Department of Computer Science
• Illinois Institute of Technology

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Course information

• Instructor XiangYang Li
• Xli_at_cs.iit.edu, 312-567-5207, SB 237D
• Homeworks?
• Exams?
• Projects?
• Gradings?

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What is this course about

• Using economics concept to solve some questions
  in computer science and vice versa

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What is economics?

• What does economics study typically?
• Traditionally, business is follows
• Business is war
• Outsmart the competition
• Capture the market share
• Make a killing brand
• Beating up supplies
• Locking up customers
• It is not enough to succeed. Others must fall.

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Nowadays

• Doing business, we have to
• Listen to customers
• Work with suppliers
• Create teams
• Establish strategic partnerships
• Even with competitors
• Business is not war,
• You do not have to blow out the other fellows
  light to let your own shine!
• but business is not peace either
• Battle with competitors over market share, fight
  suppliers for cost,
• What it is then?

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A new mindset

• Business is
• Cooperation when it comes to creating a big pie
• And competition when it comes to divide it up!
• Have to compete and cooperate at the same time
• To find a way bring together competition and
  cooperation, we use
• Game theory

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What is computer science?

• Algorithms and protocols to solve questions
  efficiently
• Algorithms
• how to solve questions
• Programming language
• tool to implement out ideas
• Architecture
• way to build the machines to solve the questions
• Computer networking
• way of exchange information
• Etc.

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What are assumptions of CS?

• Traditionally
• Single computer, single user
• So concentrate on efficiency, and cost
• Assume that the computing devices will follow our
  protocols
• Computer networking
• Still efficiency, and cost
• May consider fault tolerance, malicious devices
• Thus, security is a issue

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Not always true

• The network devices could be neither cooperative
  nor malicious
• Example wireless networking
• Peer-to-peer computing
• grid computing
• Computing devices and terminals belong to
  different users, and organizations
• Individual users are selfish
• Want to maximize its own benefit if possible

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Example Wireless networks

• No wired structure
• Self-organized
• All nodes as routers
• Broadcasted signal
• Powered by battery
• Scarce energy memory
• Mobile

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Selfish Users

• How to model this?
• Turn to game theory
• How to achieve a global system gold when selfish
  users are present?
• Economics results
• How to implement this?
• Combine with cryptography and security
• Is it efficient?
• Combine with traditional computer science wisdoms

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The game view of business

• Five basic elements of a game (PARTS)
• Players
• Added values
• Rules
• Tactics
• Scope

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Value Net
customers
Company
complementors
competitors
suppliers
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Value Net

• Complementor
• A player is your complementor if customers value
  your product more when they have the other
  players product than they have your product
  alone.
• Inter vs. Microsoft
• Competitor
• A player is your complementor if customers value
  your product less when they have the other
  players product than they have your product
  alone.
• Coca-cola vs. Pepsi-cola

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Game Theory

• An example
• Prof. Adam and 26 students
• Adam keeps 26 black cards and distributes 26 red
  cards one to each student
• Dean offer 100 for a pair of red and black cards
• Restriction students cannot gather together and
  bargain as a group with Adam.
• What will each negotiation end up?

50/50 split
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What happens if

• Another example (Barrys card game)
• Prof. Adam and 26 students
• Adam keeps 23 black cards and distributes 26 red
  cards one to each student
• Dean offer 100 for a pair of red and black cards
• Restriction students cannot gather together and
  bargain as a group with Adam.
• What will each negotiation end up?

Likely 90/10 split
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Added Value

• Your added value
• Size of the pie when you are in the game minus
  the size of the pie when you are out of the game
• Example
• Card game one
• Added value of Adam is 2600, each student is
  100, so total added value is 5200
• Barrys game
• Added value of Adam is 2300, each student is 0,
  so total added value is 2300!

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What does it tell?

• Instead of focusing on the minimum payoff you are
  willing to accept, be sure to consider how much
  the other players are willing to pay to have you
  in the game!
• Do not confuse your individual added value with
  the larger added value of a group of people in
  the same position of the game as you
• Example Barrys card game

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Rules

• Rules can change the game
• Card game example
• Rule take-it-or-leave-it negotiation a student
  can either accept or reject the offer by Adam,
  but not counter-offer, nor second offer from
  Adam.
• What will the negotiation turn out to be?
• A 50/50 split or 90/10 split or something else
• Who is more powerful now?

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Rationality and Irrationality

• Game theory assumes rational player
• Maximize its profits
• Understand the game
• No misperceptions
• No feelings of pride
• No fairness
• No jealousy, spite, vengefulness, altruism
• But the world is not like this
• So much for game theory, ?

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What is rationality

• Rationality means
• A player is rational if he does the best he can,
  given how he perceives the game, including his
  perceptions of perceptions, and how he evaluates
  the various possible outcomes of the game
• A player can percept wrong and still be rational
  he is doing the best he can given what he knows.

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Rationality as a Paradigm forInternet Computing

• Noam Nisan
• Hebrew University, Jerusalem

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Contents

• The Internet and the new face of computing
• Analyzing computing systems in equilibrium
• Designing computational mechanisms
• A defining problem Combinatorial auctions

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What is Computing?

• 20th Century
• (second half)

• 21st century
• (first decade)

The Internet
von Neumann Machine
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The Internet

• Huge dynamic heterogeneous distributed system
  normal distributed CS
• Not centrally owned different parts owned by
  different people, firms, or organizations with
  differing goals CSeconomicsgame-theory

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TCP Retransmission Rule

• Transmission Control Protocol
• Used for most Internet communication
• Breaks messages into packets, and
• assembles the packets back into messages
• Handles packet delay/loss
• TCP Retransmission Rule
• When a packet is lost, decrease transmission rate
  (by a factor of 2)
• Rational Network is congested fix it by
  reducing demand down to capacity

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TCP Retransmission Rule

• Improved Rule
• When a packet is lost, start sending each packet
  twice
• Rational Packets are lost fix it by increasing
  the probability that at least one copy of each
  packet arrives
• Why not?

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Internet Resource Sharing

• The vision
• everyone connected to the Internet should have
  access to all resources that are connected to the
  Internet
• Examples
• CPU-time
• Files
• I/O devices
• Data
• Knowledge
• Humans
• Why share?

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Electronic Commerce

• How will computers talk business?
• Using communication, security software, agents,
  
• Using standards XML, .NET, J2EE, and other
  TLAs
• What will they say to each other?
• Book X costs Y
• Bid X for Y units of stock Z
• Heres a complicated offer to you guys _at_

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Internet Computing Protocols

• Should take into account
• Computational issues
• CPU time, communication, robustness, memory,
  languages,
• Incentive issues
• Selfishness, strategies, payments, coalitions,
  risk,
• Should combine the points of view of Computer
  Science and of economics
• Should apply game theory in a computational
  context
• Rational behavior is more easily assumed from
  computers than from humans
• The strategy is in the software

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At All Protocol Levels
High level (traditional business domain)

• eCommerce eStores, auctions, exchanges, supply
  chains
• Online Services games, web-hosting, ASPs
• Information Resources music, databases
• Computational resources CPU, disk space,
  proxies, caching,
• Network Infrastructure routing, admission
  control, QoS

Low level (traditional CS domain)
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The Price of Anarchy

• Take a normal CS protocol that works well if
  everyone does what they should.
• Say Oh my god the participating computers may
  do whatever they want
• Analyze what happens when they do whatever they
  want
• Radical departure from CS want ? utility ?
  rationality ? game-theory ? equilibrium
• Aim to prove that things are still not too bad
• Or else argue against using on the Internet

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Minimizing Packet Delay
Braesss Paradox
constant delay
delay proportional to load
x
1
0
1
x

• Many smallpackets total quantity 1
• Each knows the delay situation
• Each chooses how to get to destination

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Minimizing Packet Delay
Braesss Paradox
1
0.5
0.5
1
1/2
x
1
Optimal routing (delay 1.5)
0
1
x
1

• Many smallpackets total quantity 1
• Each knows the delay situation
• Each chooses how to get to destination

0
1
Selfish routing (delay 2.0)
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The Price of Anarchy is Low
RoughgardenTardos

• Theorem for all network topologies, for all sets
  of routing requests, for all delay functions on
  the links
• If all delays are linear functions, then the
  previous example is as bad as it gets the price
  of anarchy is at most a factor of 4/3 in delay
• For general delay functions, doubling the edge
  capacities compensates for selfishness the
  price of anarchy is at most a factor of 2 in
  infrastructure

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Algorithmic Mechanism Design
NisanRonen

• Design the protocols so that they will work well
  under selfish behavior of participants
• work well the usual computational
  optimization goals
• under selfish behavior the usual
  game-theoretic concepts of equilibrium
• Use notions and techniques from the economic
  field of Mechanism Design
• Inverse game-theory
• Concentrate on incentive compatibility
  (truthfulness)
• Equilibrium is reached when all players report
  their private information truthfully
• The revelation principle shows that this is
  without loss of generality

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VCG-Mechanism in CS
Vickrey-Clarke-Groves

• Basic positive result in mechanism design
• Allow monetary transfers to/from participants
• Basic idea internalize externalities
• Each player pays/gets the total loss/benefit in
  utility he causes to all others ? All players see
  the same goal optimizing the total sum of
  players utilities

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VCG-Mechanism in CS
Vickrey-Clarke-Groves
Pay 70 (80-10) Clarke tax
Caching XXX will save me 100
Shared Cache
Caching XXX will cost me 80
Caching XXX will save me 10
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Beyond Classical Mechanism

• New domain of problems
• Parameter-complexity e.g. structure of network
• Brave-new-world disregard human conventions and
  biases
• New optimization goals
• Not just sum-of-utilities e.g. make-span in
  scheduling
• New limitations
• Computational complexity
• Distributed implementation
• Interaction with usual mechanism design often
  problematic
• New biases regarding solution concepts
• Computer scientists dont like Bayesian analysis
  real-world distributions are too different from
  those in our analysis worst-case will happen
• Computer scientists are happy with
  approximations optimality is often too hard

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Some Recent Results

• Selling digital goods (unlimited supply)
  GoldbergHartlineWright
• A randomized mechanism can approximate monopoly
  price revenue
• Scheduling jobs on unrelated machines
  NisanRonen
• No better than 2-approximation for the make-span
  is possible, but randomized mechanisms can do
  better
• Scheduling jobs on related machines
  ArcherTardos
• A polynomial time 3-approximation mechanism for
  the make-span
• Cost-sharing for multicast transmissions
  FPS
• VCG mechanism can be implemented in linear
  communication
• Auctions using a few bits
  BlumrosenNisan
• An auction with 1-bit from each player can
  achieve 98 efficiency

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Combinatorial Auctions

• Most mechanism design problems involve resource
  allocation
• The central problem in classical mechanism design
  is an auction how to allocate a single
  indivisible good?
• Abstracts many resource allocation problems
• English auction, Dutch auction, first price
  sealed-bid auction,
• Gold standard Vickreys 2nd price auction
• The emerging central problem in algorithmic
  mechanism design is a combinatorial auction how
  to allocate a collection of goods, with complex
  dependencies between them?
• Abstracts many complex resource allocation
  problems
• Involves a wide spectrum of computational and
  game-theoretic issues

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Combinatorial Auction Problem

• N indivisible non-identical items are sold
  concurrently
• k bidders compete for subsets of these items
• Each bidder j has a valuation for each set of
  items vj(S) value that j assigns to acquiring
  the set S
• vj is monotonic non-decreasing (free disposal)
• Objective Find a partition (S1Sk) of 1..N
  that maximizes the social welfare ?j vj(Sj).
• Means protocol between bidders and auctioneer
• Difficulties communication, computation,
  incentives

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Complements and Substitutes

• vj() may have complements vj(S?T) gt vj(S)vj(T)
  for some S and T.
• Extreme case single-minded bid -- will only
  pay for a complete package -- pay p for the set S
  but pay nothing for anything else
• vj() may have substitutes vj(S?T) lt vj(S)vj(T)
  for some disjoint S and T.
• Extreme case unit demand bid -- will pay for
  at most a single item the price may depend on
  the item

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Routing as Combinatorial Auction
Bidder A
Destination
Bidder B
Bidder C

• Each bidder wants to buy some path to the
  destination
• Each link is an item

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The FCC Spectrum Auctions

• The FCC auctions spectrum licenses for many
  geographic regions and various frequency bands
• These auctions have raised billions of dollars
• The value of a license to a bidder depends on the
  other licenses it holds
• Currently licenses are
• sold in a simultaneous
• auction
• USA Congress mandated
• that the next spectrum
• auction be made
• combinatorial.

3.1-3.2GHz
3.1-3.2GHz
3.2-3.3GHz
3.2-3.3GHz
3.3-3.4GHz
3.1-3.2GHz
3.2-3.3GHz
3.1-3.2GHz
3.1-3.2GHz
3.2-3.3GHz
3.2-3.3GHz
3.3-3.4GHz
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Basic Mechanism Approach

• Basic Solution
• Each bidder sends vj() to auctioneer.
• Auctioneer finds the partition that maximizes ?j
  vj(Sj).
• Auctioneer allocates Sj to each bidder j
• Auctioneer charges VCG payments ensures
  incentive compatibility
• Computational difficulties
• Bidding How to send vj()? Requires
  communication of
• numbers impractical
• Allocation How can the auctioneer find an
  optimal allocation? The problem is
  computationally intractable (even to approximate
  well)

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Bidding Languages

• The auction must fix a language for
  representing valuations. All bidders will use
  that language to express their valuations
• Language must be expressive express all
  reasonable valuations succinctly
• Language must be simple computationally easy to
  manage valuations (represent, determine
  allocation,)
• Proposed languages use package bids, OR, XOR
• (left-sock right-sock 5)
• OR
• ( (Red-shirt 10) XOR (blue-shirt 9))
• Different bidding languages have different power
• What should the FCC allow?

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Iterative Auctions

• Definition
• The demand of valuation v at item prices p1 pn
  is the set S that maximizes the benefit v(S)-?i?
  S pi
• A Walrasian equilibrium is an allocation S1Sm
  and item prices p1 pn such that each Sj is
  the demand of vj at these prices
• Fact Any Walrasian equilibrium gives an optimal
  allocation
• Algorithm
  DemangeGaleSotomayor
• initialize prices of all items to 0
• repeat if an item is demanded by more than one
  bidder, increase the price a little until a
  Walrasian equilibrium is reached
• Theorem This works if valuations are gross
  substitutes KelsoCrawford
• Theorem In general, exponential communication
  (equivalently, an exponential number of prices)
  is needed
  NisanSegal

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Allocation Algorithms

• The allocation problem is computationally
  intractable
• Approaches for overcoming computational
  difficulty
• Solve (or approximate) special tractable cases
• Gross substitutes
  KelsoCrawford
• Sub-modular (2-approximation)
  LehmannLehmannNisan
• Linear order on items
  RothkopfPekecHarstad
• Heuristics that obtain optimal allocations and
  run reasonable fast
• Practical for 100s of items
  CABOB -- Sandholm et al.
• Heuristics that run quickly and find reasonably
  good solutions
• A few loss for 1000s of items
  ZurelNisan
• Use the usual tools of combinatorial optimization
• LP relaxation
• Branch-and-bound, cutting-planes
• Local search
• Dynamic programming

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Incentives vs. Allocation

• Challenge find a mechanism that obtains
  reasonably good allocations and is
  computationally efficient.
• Key problem Algorithms that find sub-optimal
  allocations do not yield incentive compatible
  mechanisms
• Attaching VCG payments to sub-optimal algorithms
  essentially never yields incentive compatibility
  NisanRonen
• The only known incentive compatible mechanisms
  are VCG for complete spaces with at least 3
  possible outcomes only VCG mechanisms exist.
  Roberts,
  GreenLaffont
• Special case single minded bidders have a
  single valuation parameter and desire a single
  package
• A Computationally efficient incentive compatible
  mechanism exists
  LehmannOcallaghanShoham
  
• Open problem Find any non-VCG mechanism for any
  multi-dimensional valuation space